Risk and Uncertainty*
M
by Pablo A. Guerron-Quintana
any news reports and economic experts talk
about uncertainty. But what does the word
mean in an economic context? Specifically,
what do economists have in mind when they
talk about it? In this article, Pablo Guerron-Quintana
discusses the concepts of risk and uncertainty, what
the difference is between the two terms, and why their
presence in the economy may have widespread effects. He
also talks about measuring risk at the aggregate level —
that is, risk that affects all participants in the economy
— and he reviews the various types of risk measures that
economists have proposed.
Many news reports and economic experts talk about uncertainty.
Take, for example, the recent discussion about the U.S. budget situation.
Although several proposals have been
offered that aim to achieve a fiscally
sustainable budget, we do not know
with certainty which measures will
ultimately be adopted or their timeline.
According to some economists, this
uncertainty seems to have contributed
to a slowdown in investment, hiring,
and economic activity and has the
potential to affect our standard of liv-
Pablo GuerronQuintana is an
economic advisor
and economist
in the Research
Department of
the Philadelphia
Fed. This article
is available free
of charge at www.philadelphiafed.org/
research-and-data/publications.
10 Q1 2012 Business Review
ing. But what does uncertainty mean?
More important, what do economists
have in mind when they talk about it?
This article will discuss the concepts of risk and uncertainty and why
their presence in the economy may
have widespread effects. We will also
talk about measuring risk at the aggregate level, that is, risk that affects
all participants in the economy. Different measures of this aggregate risk
have been proposed: (1) disagreement
among forecasters, (2) stock market
volatility, (3) interest rate volatility,
and (4) tax rate volatility. Each of
these measures has its pros and cons.
Over the years, the concepts of
risk and uncertainty have often been
used interchangeably in the popular
press, but economists have long distin-
*The views expressed here are those of the
author and do not necessarily represent
the views of the Federal Reserve Bank of
Philadelphia or the Federal Reserve System.
guished between the two. Indeed, the
concept of uncertainty was probably
first introduced to economics by Frank
Knight in his 1921 treatise Risk, Uncertainty, and Profit.1 Knight drew the
distinction between risk – unknown
outcomes whose odds of happening
can be measured or at least learned
about – and uncertainty – uncertain
events that we do not even know how
to describe. Economists often label
these ideas Knightian risk and Knightian
uncertainty, although sometimes they
are called objective uncertainty and subjective uncertainty. (See Uncertainty Is
Different from Risk.)
Risk can affect us at an individual
level. In our daily lives, we get hit by
unanticipated events such as accidents
or diseases or being hired for a dream
job or even winning the lottery. While
the last two examples are pleasant
surprises, the first two events involve
physical and mental strain and potential monetary losses. Since most of us
dislike facing stressful situations, we
modify our behavior when bad luck
knocks on our door. For instance, we
buy insurance to protect us from the
monetary loss we could sustain from
car accidents or the cancellation of a
vacation trip. Furthermore, the knowledge that we may lose our job can be
strong enough to deter us from taking
that well-deserved vacation. All of
these examples provide powerful reasons why we may want to learn more
about risk.
1
The interest in uncertainty in economics seems to coincide with a broader wave of
interest in the topic in science, as reflected
by Heisenberg’s 1927 work on uncertainty in
physics.
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Uncertainty Is Different from Risk
T
o understand the difference between
risk and uncertainty, let’s consider the
experiment of flipping a fair coin (Case
A). In this experiment, the unknown is
whether the coin will land heads or tails.
Since we are dealing with a fair coin,
we know that the odds of heads after each flip are 50-50.
That is, if we were to flip the coin let’s say 100 times,
the coin would land, on average, 50 times heads and 50
times tails. The crucial insight from this experiment is
the observation that we know exactly the odds of each of
the possible events: 50 percent heads and 50 percent tails.
Furthermore, we have this knowledge before starting the
experiment. This is precisely the essence of risk: We can
describe the odds of the unknowns.
Now let’s consider an alternative experiment (Case
B). As before, we are interested in learning the result of
flipping a coin. The key difference is that we know the
coin is no longer fair, but we do not know the odds of obtaining heads. Furthermore, the coin is replaced by a new
(and unfair) coin after each flip.a Under this scenario, the
only thing we know is that the coin will land either heads
or tails. If we were thinking about flipping the coin 100
times, we could not (before we start the experiment) tell
how many times the coin will land on heads. This is an
example of Knight’s uncertainty.
Another way to see the difference between risk and
uncertainty is as follows. Suppose 100 people are asked to
place odds on the coin landing on heads in experiments
A and B. In Case A, people would agree that the odds are
50-50, but in Case B, their assessment would range from
0 to 100 percent. Furthermore, those people would prefer
to bet on getting heads in experiment A than on getting
heads in experiment B.b
The concept of uncertainty goes beyond those situations in which we cannot establish the likelihood of
events. It also includes cases when we do not even know
the outcomes. An extreme example is as follows. Imagine that a person from the Midwest decides to vacation
in Volcanoland, a fictitious country buffeted by constant volcanic and seismic activity. If a sudden volcanic
eruption surprises our friendly Midwesterner, his lack of
knowledge and experience with volcanoes makes his immediate future quite uncertain. How long is the eruption
going to last? Does he have enough food and water? Is his
shelter safe? Our friend is asking himself these questions
because he is uncertain about the possible outcomes from
an eruption. In this example, we are aware that something has happened (an eruption), but we do not know its
potential consequences.
Assessing the impact of uncertainty is trickier. The
reason, as explained in the introduction, is that one cannot assign probabilities to the possible outcomes or one
does not know all the possible outcomes. This lack of
knowledge means that the consequences of uncertainty
can range from nothing to vast monetary losses.c To see
this point, let’s reconsider the case of tossing an unfair
coin 100 times. Suppose that we get $1 each time the
coin lands on heads and pay $1 otherwise. What we know
before flipping the coin is that we may make as much as
$100 (all trials land on heads) or we may lose $100 (all trials land on tails). Furthermore, any payment in between is
possible. The unfair nature of the coin makes it impossible for us to determine the expected payoff from entering
into this contest.
Now consider the case of the Midwesterner facing a
volcanic eruption in Volcanoland. What are the potential
consequences for this person? On the one hand, the only
annoyance our friend may face is ashes falling from the sky.
The uniqueness of this event also implies that if the eruption turns out to be violent, our friend may be risking a lot
more than a spoiled vacation. As with the case of the coin
tossing exercise, we cannot determine beforehand the potential losses from being exposed to a geologic contingency.
This assumption is needed to ensure that we cannot learn the odds of getting heads by repeatedly flipping the coin. If this were the case, after
the learning stage, we would be in a case essentially the same as that of flipping a fair coin, whose odds of landing on heads are a known constant,
although different from 50-50.
a
b
This preference to act on known rather than unknown probabilities is called the Ellsberg paradox (Ellsberg, 1961).
c
Larry Epstein and Tan Wang provide a comprehensive analysis of uncertainty.
The idea that risk can affect not
only our daily lives but also the overall
economy is not new. Indeed, in the
1930s, the English economist John
Maynard Keynes indicated that investors’ mood could lead to economic
www.philadelphiafed.org
downturns. He reasoned that investment was in part driven by investors’
view of the economy. If they are uncertain about the economy’s prospects,
they reduce investment, triggering a
downturn.
ASSESSING THE IMPACT OF
RISK
Risk can affect the economy in
at least two ways: through investment
and/or through savings. The current
“risky” scenario about where house
Business Review Q1 2012 11
prices are heading (up, down, or stable)
and whether interest rates are going up
makes the investment decision nontrivial. The optimal response to risky situations may be to wait and see. In other
words, households choose to delay investment (buying a house) until things
calm down. The reason is that individuals may face an adverse scenario
with high interest rates and a contraction in house prices. This possibility
makes investment quite risky, inducing
households to wait for better times.
Put differently, when facing uncertain
scenarios, investors must decide on the
timing of their investment decisions.2
But risk can affect savings as
well. Imagine that you owe credit card
debt and that your monthly payment
is $200. Suddenly, your credit card
company announces that interest rates
may go up next month. Moreover, the
company announces that if interest
rates go up, interest payments will
most likely double for some customers. Under these circumstances, you
may find it desirable to consume less
today and use that extra cash to repay
part of your debt. The additional cash
should be used to repay part or all of
your debt. If you choose otherwise, you
may face credit card payments as high
as $400 next month. Even more worrisome, because of those large payments,
you may have to cut your consumption
by a large amount tomorrow.
The previous example can be
extended to the case of countries.
Imagine that a country issues debt to
cover part of its investment and other
expenses. If the country’s creditors
disclose that interest rates may change
next month, the country may want to
repay part of its debt to reduce the future burden of interest rate payments.
In order to pay more today, the country needs to produce more. But inCommitting to early investment brings in extra returns, while waiting is beneficial because
of access to additional information. See the
article by Ben Bernanke.
2
12 Q1 2012 Business Review
creasing production takes time (hiring
more workers, building factories, and
so on). This means that the only way
the country can repay its obligations is
by cutting its expenses, that is, reducing consumption and investment. In
other words, the country needs to sell
more goods abroad (increase exports)
and buy fewer goods from abroad
(decrease imports). Since not all goods
can be exported (for example, haircuts, legal and medical services, and
houses), some industries will be forced
to produce less. This decline in production will result in higher unemployment for a segment of the population.
Obviously, how our decisions
change when we face risky situations
depends on our attitudes toward risk.
For instance, a gambler (a person who
loves taking additional risk) may well
opt to purchase a home with the hope
that prices will eventually recover.
The gambler understands there is a
big chance that prices may not recover
for a while. Yet the mere fact of taking
a chance gives him satisfaction and
hence drives him to bet on the housing
market. In contrast, a cautious person
may choose not to gamble on the
housing market and may refrain from
buying a house these days. For the
cautious person, the potential losses far
outweigh the benefits from buying a
house in a depressed market and hoping it will recover.3
In the context of an economic model, whereas
a gambler would correspond to a person whose
preferences are described by a linear utility
function, a risk-averse person — a cautious
person — has a concave utility function. If the
two persons were to invest in a risky project,
such as buying stocks, the gambler would
care only about the project’s payoff, since he
considers only his total consumption. He would
take on whatever project offers large rewards,
even though it may also entail large losses. In
contrast, the cautious person would also factor
in the odds that the project could fail. Even if
the promised payoff is large, a risk-averse person
may opt out of the project because the odds that
it will fail are too big. In other words, he would
rather have fewer swings in his income even if
that means a lower average income.
3
Since the presence of risk can
entail monetary losses, people try to
protect themselves by buying insurance. In simple terms, an insurance
contract transfers the risk of loss from
the policy holder to the insurer, usually
a large company. The contract typically sets a small and regular payment
to be made by the insured person. In
How our decisions
change when we
face risky situations
depends on our
attitudes toward risk.
exchange, the insurer promises to pay
the policy holder a given monetary
amount if certain events happen, as
defined in the contract. Some examples include having a car accident,
having a vacation trip cancelled, or being laid off from a job. In this last case,
the insured person is a worker and the
insurer is the federal government and/
or the state.
But accidents happen; people get
sick; workers get laid off. More important, these unpleasant events happen
more frequently than we would like.
So why do insurance companies exist?
One reason is that the insurer and the
policy holder may have different views
about the odds that an event will occur. To illustrate my point, imagine
a person who is afraid of flying. His
pessimistic view about air transportation leads him to look for insurance.
In contrast, an insurance company
knows that flying is the safest medium
of transportation. The odds of an incident are very small, so the insurer is
more than willing to extend a policy to
the concerned flyer.4
Even if the insurer and the policy
holder have the same assessment of
Indeed, the odds of dying in a plane crash for
the average American is about 1 in 11 million.
4
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the odds that an event will occur, the
insurer may still be willing to extend a
policy to the insured person. For example, this is the case with car insurance.
For instance, a car owner who lives in
a crowded city has a greater probability of being involved in an accident,
a situation that requires payments
from the insurer to the policy holder.5
To reduce their exposure to this type
of event, insurance companies offer
policies to a large number of drivers.
Since car accidents tend to be isolated
events, the likelihood of an insurance
company facing accident claims from
all its insured customers at the same
time is very low. Hence, although the
insurer may need to make frequent
payments, the insurer is also receiving
payments (premiums) from those policy holders who have not been involved
in an accident or the deductibles from
those who have been. In this way, the
insurance company has enough funds
to pay its insured customers who have
car accidents.
MEASURING RISK:
SOME BASICS
From the discussion in the previous sections, it should be clear that risk
can influence our lives. Obviously, the
influence of risk depends on the circumstances under which it affects us.
For example, consider the risk associated with the weather. Under normal
circumstances, a day with bad weather
means that we may be late getting
to work; that is, the expected loss —
the risk — is low. But in some cases,
the risk can be high. Imagine if you
missed an interview for your dream job
because of bad weather. The stakes are
even higher when we think of the risk
associated with buying a house or a
government that is considering issuing
bonds. In the first case, risk arises from
Eric Smith and Randall Wright analyze the
interesting issue of why car insurance is so
expensive in certain metropolitan areas.
5
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fluctuations in the price of houses, and
in the second case, the variability of
interest rates (and hence the cost of issuing bonds) matters. The bottom line
in these examples is that understanding the consequences of risk requires
measuring it. Once we have a measurement, we can then take actions such as
postponing the purchase of a house or
buying insurance.
Economists have proposed different measures of risk: (1) disagreement
among forecasters, (2) stock market
volatility, (3) fluctuations in interest
rates, and (4) fluctuations in tax rates.6
Disagreement Among Forecasters. Imagine that today is a bright
and sunny day. If you were asked to
forecast the weather for the afternoon,
assuming that you don’t have access to
a weather forecast service, you would
most likely answer “a sunny afternoon.” In fact, everyone would agree
with you. Now imagine that today is
sunny, but a few clouds lurk on the
horizon. The presence of those clouds
makes forecasting the weather for this
afternoon more difficult. Some people
may forecast a sunny afternoon; others
may guess a cloudy but dry afternoon,
while a third group may forecast a
rainy afternoon.
The idea behind the last example
is that periods of elevated risk are associated with very imprecise forecasts
about future events. In other words, the
more risky the event, the harder it is to
forecast and, therefore, the larger the
disagreement among forecasters. In our
example, the risky situation arises from
those clouds on the horizon. Rather
than the weather, economists are frequently interested in the total number
of goods that an economy produces,
that is, a country’s gross domestic product (GDP). Hence, our first measure
6
Economists have proposed other ways to
measure risk. The interested reader is invited
to consult the article by Nicholas Bloom, Max
Floetotto, and Nir Jaimovich.
of risk comes from the forecasters’ disagreement about what the growth rate
of GDP is going to be a year from now.
This measure is published quarterly by
the Federal Reserve Bank of Philadelphia in the Survey of Professional
Forecasters. It is the percent difference
between the 75th and 25th percentiles
of the one-year-ahead projections for
U.S. real gross domestic product.
Figure 1 shows that the degree of
riskiness (measured by forecast dispersion) was large in the 1970s, in particular, during the oil embargo of 1974 and
at the beginning of the Fed’s disinflationary era around 1979. The figure
also suggests that disagreement has
diminished during the 1990s and the
first half of the 2000s. This decline coincides with what economists call the
Great Moderation, that is, the period
between 1984 and 2007 characterized
by two relatively mild recessions and,
in general, moderate fluctuations in
the economy. During this period, the
increasing agreement among forecasters resulted from the more stable, and
thus more predictable, economy. This
reasoning has led some observers to
argue that the prolonged boom prior
to the recent crisis arose from a stable
economy.7 This stability stimulated
consumption and investment. To meet
higher demand, firms increased their
production by expanding their facilities
(additional investment) and increasing
employment.
Another look at Figure 1 reveals a
rise in risk since the start of the 2007
financial crisis. The highest level of
risk happens by the end of 2008, which
coincides with the collapse of Lehman
Brothers. What makes the 2007-2010
episode different from other periods over the last 20 years is that risk
remained heightened for more than a
year. With so much risk around, it is
not surprising that firms and house7
See the study by James Stock and Mark
Watson.
Business Review Q1 2012 13
holds postponed their purchasing and
investing decisions. Interestingly, the
improvement in the economy of recent
months seems to coincide with a decline in risk. Note how the measure at
the end of 2010 is getting close to its
pre-crisis levels. 8
A simple way to make sense of
the numbers in Figure 1 is as follows.
You and I own an apple tree, and we
are interested in forecasting our tree’s
annual production. Furthermore, let’s
suppose that our disagreement over
the years is represented by Figure 1. In
the first quarter of 1980, our forecast
disagreement reached an all-time high
of almost three. This means that at
that moment, if I had forecasted that
our tree would produce 100 apples in
1981, your forecast would have been
103.9 Now, let us move forward to
March 2007 when our disagreement
was the lowest (0.4). At that point, if
my forecast was 100 apples, you would
have forecasted 100.4 apples. We were
essentially making the same forecast.
After the turbulent financial events
of 2008, our disagreement rose to 1.5
apples and remained at that level for
most of 2009.
Stock Market Fluctuations. During times of high risk, new information about the state of a company
(for instance, its profits and prospects
for future projects) tends to arrive
frequently. In response to the arrival
of information, investors buy and sell
stocks in the company quite frequently.
As a result, the stock price of the
company fluctuates substantially in the
short run. The more uncertain inves-
8
Of course, the causality could go the other
way around: Periods of high growth promote
tranquil times and hence low risk. In a recent
paper, Scott Baker and Nicholas Bloom use
stock market information from several countries
to argue that the causality runs from risk to
economic growth.
9
For simplicity, I assume in this example that
I am the person making the conservative
forecast.
14 Q1 2012 Business Review
FIGURE 1
U.S. Real GDP Growth Forecast Dispersion
Source: Survey of Professional Forecasters from the Federal Reserve Bank of Philadelphia,
quarterly data 1970:Q1 - 2010:Q3
tors are about a company, the more
they bet up or down on that company’s
stock. Hence, our second measure of
risk comes from the variability (volatility) in the stock prices of companies
publicly traded on the New York stock
exchange. This indicator (displayed in
Figure 2) is closely tracked by financial
practitioners, since it is considered a
measure of investor sentiment: The
higher stock market volatility is, the
more pessimistic investors are, that is,
the greater the expectation that the
market will fall. But recall that worried
investors tend to wait and see. Hence,
a sudden and persistent increase in
stock market volatility may be signaling weak demand down the road and
a potential contraction in the overall
economy. It is this linkage between
stock market volatility and economic
activity that has made our second
measure of risk popular both in academia and in policy circles. (See the
studies by Nicholas Bloom.)
Based on Figure 2, it is clear that
periods of economic and financial
turmoil are associated with strong
fluctuations in the stock market.10
For example, the market was more
volatile during the oil embargo of 1974
or the Asian financial crisis and the
collapse of dot-com companies in the
late 1990s. Similarly, the stock market
crash of October 1987 resulted in a
large spike, albeit temporary, of our
measure of risk.11 Figure 2 also shows
that the U.S. economy enjoyed a
period of tranquility and low risk starting around 1988 and extending into
1997. More recently, the onset of the
mortgage crisis (2007) and the demise
of Bear Stearns (March 2008) and
The U.S. stock market volatility is taken from
the article by Nicholas Bloom. The measure
corresponds to the Chicago Board of Options
Exchange VXO index of implied volatility from
1986 onward. Prior to 1986, actual volatility in
monthly returns is calculated as the monthly
standard deviation of the daily S&P 500 index.
10
Some economic observers attributed this
quick reversal in risk to the Federal Reserve System’s (and its then-Chairman Alan
Greenspan’s) swift actions to support financial
markets. See the paper by Mark Carlson.
11
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FIGURE 2
Stock Market Volatility: 1963 - 2011
Source: Nicholas Bloom. Monthly data 1963:M1 - 2011:M1
Lehman Brothers (September 2008)
shook financial markets. Figure 2
reveals that our measure of risk rose in
response to those events. In fact, risk
reached its all-time high in October
2008 and remained elevated for most
of 2009.
An advantage of the stock market volatility measure is that it goes
back to the 1960s and therefore allows us to illustrate how risk responds
to political events. For example, the
spike in risk at the beginning of 1964
coincides with President Kennedy’s
assassination. Moving forward, the
Cambodian campaign and the Kent
State shooting in 1970 pushed risk
up.12 Finally, the attacks on the World
The shooting at Kent State University (Kent,
Ohio) resulted in four people being killed and
nine others wounded. Students were protesting the Vietnam War. The shooting happened
just days after President Nixon announced
the launch of the Cambodian incursion. This
military action was intended to defeat North
Vietnam’s troops using the eastern part of Cambodia to stage attacks on South Vietnam.
12
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Trade Center and the Pentagon in
September 2001 are also associated
with more risk in the market.
To make sense of the numbers
in Figure 2, let’s consider the following example. You own stock in a large
group of leading companies in diverse
industries in the U.S.13 You are interested in learning the odds that the
return on your portfolio will move up
or down by 10 percent next month. If
you were wondering this in October
2008 and asking about your return in
November 2008, the results in Figure 2
imply that the odds are roughly 50 percent that the return on your portfolio
will move up or down by 10 percent. In
contrast, if you were asking the same
question in December 2006, you would
conclude that the chances that your
returns would go up or down by 10
percent is practically 100 percent. This
More precisely, you own stock in each of the
500 companies that are part of the S&P 500
index.
13
means that you are almost certain that
the returns to your portfolio would
not exceed +/–10 percent in January
2007.14 This is because stock market
volatility was so low in December 2006
that sudden changes in stock prices
and hence abrupt movements in stock
returns were very unlikely.
I must stress that when stock
market volatility is high, it does not
necessarily mean that the market expects a sharp decline in stock prices.
It only means that the market expects
that sudden price movements in either
direction (up or down) are more likely.
Since most people tend to be concerned
about losses, investors seem to dislike
high stock market volatility (high risk)
because it signals that a sharp collapse
in stock prices is more likely.
Interest Rate Volatility. An alternative description of risk results from
direct measures of fluctuations in interest rates. Such measures have been
used recently in papers that try to assess the impact of risk on the economy.
(See my paper with Jesus FernandezVillaverde, Juan Rubio-Ramirez, and
Martin Uribe.)
The idea behind the measure of
interest-rate volatility is that people
tend to trade (sell or buy) bonds very
frequently during periods of high
risk. This frequent exchange of bonds
makes their price fluctuate substantially, which results in large swings in
interest rates.15 Hence, periods of large
These numbers were computed following the
interpretation outlined in the study by Robert
Whaley. Succinctly, the probability is computed
by asking ourselves what is the probability that a
random normal variable falls within σ standard
deviations from 0. Here, σ =
, Er is the
anticipated movement in the asset return, and
VIX is the stock market volatility in Figure 2. In
our first example, the values are Er = 10 percent
and VIX = 50 percent, which implies σ = 0.69
or a probability of 50 percent. If the VIX drops
to 10 percent, then σ = 3.46, which, based on a
normal distribution, implies a probability of 1.
14
The price and interest rate of a bond are inversely related, so any movement in prices translates directly to fluctuations in interest rates.
15
Business Review Q1 2012 15
fluctuations (volatility) in interest rates
are interpreted as episodes in which
risk is high. As an example, Figure 3
illustrates the evolution of our interestrate risk measure for Argentina. A
quick look at this figure reveals that
risk in Argentina was high in early
1998 and again during the period 2001
to 2004.16
To understand these changes in
risk, some background information
about Argentina is necessary. The
1990s were mostly a boom period for
Argentineans (presumably due to
economic reforms introduced early
in that decade). The country experienced sustained economic growth and
stable prices. In the eyes of investors,
Argentina was an example for other
countries to follow. However, this
stability started to collapse around
1998 when several East Asian countries experienced financial difficulties,
forcing them to stop payments on their
debt obligations to international lenders. Although Argentina was in better
economic health than the defaulting
countries, nervous lenders worldwide
feared that Argentina (and other
countries in South America) would
follow suit. Investors could not assess
how much the Argentinean economy
would be affected by the collapse of
Asian economies. Ultimately, Argentinean debt was heavily traded during
this period, which resulted in sudden
fluctuations in interest rates and hence
a spike in risk.17 As time went by, it was
clear that Argentina would be able to
The Argentinean interest rate is the sum of
the real rate on the three-month U.S. Treasury
bill plus Argentina’s Emerging Markets Bond
Index+ (EMBI+). The T-bill rate is taken from
the St. Louis Fed’s FRED database. The EMBI+
index is published monthly by J.P. Morgan. The
risk measure in Figure 3 is constructed using the
econometric approach described in my paper
with Jesus Fernandez-Villaverde, Juan RubioRamirez, and Martin Uribe.
16
Interestingly, risk in the U.S. was also elevated
in the late 1990s, as shown in Figure 2.
17
16 Q1 2012 Business Review
FIGURE 3
Interest Rate Volatility in Argentina
Source: Jesus Fernandez-Villaverde et al. (2011). Monthly data 1997:M12 - 2004:M9
meet its obligations, so the country became less risky. This is reflected by the
drop in our measure of risk between
1999 and 2000.
After almost a decade of boom,
the Argentinean economy slowed
down in 2000 and contracted in
2001. At the same time, the Argentinean currency (the peso) was greatly
overvalued, which made Argentina’s
products more expensive than those
imported from abroad and hence reduced its exports. This decline in production and lack of exports meant that
fewer resources were available to repay
debt. In response, investors demanded
higher interest rates for loans extended
to Argentina. These tough economic
conditions led the country to default
(stop paying principal and interest on
its debt), which triggered the spike in
our measure of risk by the end of 2001.
Risk remained heightened for the next
two years as the country continued to
miss payments on its obligations.
Figure 3 shows that risk started to
decline around 2003. This improve-
ment seems to coincide with the beginning of Nestor Kirchner’s presidency. To some observers, the economic
policies implemented by Kirchner and
his predecessor (Eduardo Duhalde)
paved the way to an orderly recovery.
By the end of our sample period (August 2004), risk had reached its lowest
level in three years, since international
investors anticipated that Argentina
would eventually try to meet or renegotiate its debt obligations. Indeed,
in 2005, the country restructured its
obligations with roughly 75 percent of
its debt holders.18
A simple way to make sense of
the numbers in Figure 3 is as follows.
Imagine that you are living in Argentina in August 2000. You just bought a
new car with an adjustable interest rate
loan. The prevailing annual interest
rate at that point was about 8 percent.
Old bonds were replaced by new debt with
longer maturity and nominal value of between
25 and 35 percent of the original debt.
18
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FIGURE 4
Capital Tax Rate Volatility
Source: Jesus Fernandez-Villaverde et al. (2012). Quarterly data 1970:Q1 - 2010:Q1
By construction, Figure 3 tells us that
there was a 68 percent chance that
the interest rate would go up or down
by 2 percentage points. This means
that in August 2000 you believed that
your interest rate could be as high as
10 percent or as low as 6 percent in
September 2000. Let’s move forward
to December 2001. Our risk measure
indicates that with a probability of 68
percent, your interest rate could jump
up or down by 7 percentage points!
This means that, all other things
equal, you could have faced interest
rates as high as 15 percent on your
car loan. For a principal of $10,000,
these numbers imply that whereas your
monthly payment in September 2001
could have been as high as $800, your
payment in December 2001 could have
been $1,170.19 Clearly, there is a non-
An annual interest rate of 10 percent is
roughly equivalent to 0.8 percent on a monthly
basis. Similarly, a 15 percent annual interest rate translates into a monthly rate of 11.7
percent.
19
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trivial increase in your payments when
the economy gets riskier.
The Argentinean example teaches
us two important lessons about risk.
First, risk can be contagious. Even
though Argentina was a well-positioned economy in the late 1990s, it
suffered from substantial fluctuations
in its risk index. In this case, risk
was imported from financial turmoil
abroad. The second lesson is that risk
can arise from domestic factors. The
economic instability of Argentina and
its subsequent inability to meet its obligations at the end of 2001 resulted in
the massive spike in Argentina’s risk.
Here, there were no foreign elements
triggering the sudden change in interest rate fluctuations.
Tax Rate Volatility. A final
description of risk comes from fluctuations in tax rates. This notion was recently proposed in my paper with Jesus
Fernandez-Villaverde, Keith Kuester,
and Juan Rubio-Ramirez. The idea is
that governments tend to overhaul tax
systems during periods of fiscal strain
(such as the current one), which results
in substantial fluctuations in tax rates.
The worse the fiscal situation, the
more volatile the taxes are.
Figure 4 presents our new risk
measure based on the volatility of the
capital tax rate in the United States.20
The measure shows that risk associated with fiscal policy was high during
President Clinton’s first term. Indeed,
the Omnibus Budget Reconciliation
Act, which was signed into law in
1993, raised tax rates, affecting both
individuals and businesses. Similarly,
our risk measure rises during President
George W. Bush’s tax cuts in the early
2000s.
It is also apparent from Figure
4 that the recent financial crisis has
heightened the fiscal-related risk. Risk
was high between 2007 and 2009; only
in early 2010 does risk linked to fiscal
policy go back to pre-crisis levels.
In our paper we show that risk
associated with fiscal policy can slow
down the economy. The reason is that
volatility makes it difficult to forecast future tax rates on capital. As a
consequence, investors considering
investing in new projects may opt to
wait or completely skip those projects.
This is because investors fear that large
volatility may ultimately translate into
large future taxes, thus reducing the
profitability of their investments. If the
capital tax rate volatility is sufficiently
high, the decline in investment can
induce a general contraction in economic activity (lower production and
higher unemployment).
Imagine that you are back in the
fourth quarter of 1995. You just invested in a new project whose payoffs
are taxed at 35 percent. By construc-
The tax rate on capital corresponds to aggregate effective rates on capital income. The
risk measure in Figure 4 is constructed using
the econometric approach described in my
paper with Fernandez-Villaverde, Kuester, and
Rubio-Ramirez.
20
Business Review Q1 2012 17
tion, Figure 4 tells us that there was
a 68 percent chance that the capital
tax rate would go up or down by 0.5
percentage point. This means that in
December 1995, you believed that the
tax rate on capital income could be as
high as 35.5 percent or as low as 34.5
percent in March 1996. Let’s move forward to December 2001. Our risk measure indicates that with a probability
of 68 percent, your tax rate could jump
up or down by 1.4 percentage points!
This means that, all other things
equal, you could have faced a tax rate
on capital as high as 36.4 percent.
This sudden change in the tax rate is
sufficient to deter investment, at least
temporarily, and induce a contraction
in economic activity.
SUMMARY
This article introduced the economic concepts of risk and uncertainty. It provides clear and simple
definitions and examples of risk and
uncertainty. Furthermore, this article
shows that risk can have important
consequences for economic activity.
For example, an increase in the volatility of interest rates at which countries
borrow can induce a contraction in
consumption and investment.
Economists have proposed alternative measures of risk: (1) disagreement
among forecasters, (2) stock market
volatility, (3) interest rate volatility,
and (4) tax rate volatility. All of these
measures indicate that risk increases
during periods of political and economic turmoil, such as President Kennedy’s
assassination, the 1987 stock market
crash, and the recent financial crisis.
Furthermore, these measures show that
risk in the U.S. was low during the late
1980s and the first half of the 1990s. BR
Epstein, Larry, and Tan Wang. “Intertemporal Asset Pricing under Knightian
Uncertainty,” Econometrica, 63 (1994).
LeRoy, Stephen, and Larry Singell. “Knight
on Risk and Uncertainty,” Journal of Political Economy 95:2 (1987), pp. 394-406.
Fernandez-Villaverde, Jesus, Pablo Guerron-Quintana, Juan Rubio-Ramirez, and
Martin Uribe. “Risk Matters: The Real
Effects of Volatility Shocks,” American
Economic Review, 10:6 (2011), pp. 2530-61.
Santomero, Anthony. “Monetary Policy
in the Post 9/11 Environment: Stability
Through Change,” speech for the Global
Interdependence Center’s 22nd Annual
International and Monetary Trade Conference, held at the Federal Reserve Bank of
Philadelphia, October 2, 2003.
REFERENCES
Baker, Scott, and Nicholas Bloom. “Does
Uncertainty Drive Business Cycles? Using Disasters as a Natural Experiment,”
mimeo, Stanford University.
Bernanke, Ben. “Irreversibility, Uncertainty, and Cyclical Investment,” Quarterly
Journal of Economics 97:1 (1983).
Bloom, Nicholas. “The Impact of Uncertainty Shocks,” Econometrica, 77:3 (May
2009), pp. 623-85.
Bloom, Nicholas, Max Floetotto, and Nir
Jaimovich. “Really Uncertain Business Cycles,” mimeo, Stanford University (2009).
Carlson, Mark. “A Brief History of the
1987 Stock Market Crash,” Board of
Governors of the Federal Reserve System,
Finance and Economics Discussion Series
2007-13 (2007).
Ellsberg, Daniel. “Risk, Ambiguity, and
the Savage Axioms,” Quarterly Journal of
Economics 75:4 (1961).
18 Q1 2012 Business Review
Fernandez-Villaverde, Jesus, Pablo Guerron-Quintana, Keith Kuester, and Juan
Rubio-Ramirez. “Fiscal Volatility Shocks
and Economic Activity,” Federal Reserve
Bank of Philadelphia Working Paper 1132/R (January 2012).
Smith, Eric, and Randall Wright. “Why
Is Automobile Insurance in Philadelphia
So Damn Expensive?” American Economic
Review, 82 (1992), pp. 756-72.
Heisenberg, Werner. “Quantum Theory
and Measurement,” Zeitschrift für Physik 43
(1927), pp. 172–98.
Stock, James and Mark Watson. “Has
the Business Cycle Changed and Why?,”
NBER Macroeconomics Annual (2002).
Knight, Frank H. Risk, Uncertainty, and
Profit. Boston: Houghton Mifflin, 1921.
Whaley, Robert. “Understanding the VIX,”
Journal of Portfolio Management, 35 (Spring
2009), pp. 98-105.
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